A micro-magnetic simulation is a method used in theoretical calculation of a magnetic body or a magnetic material. In the micro-magnetic simulation, for example, as illustrated in FIG. 1, a magnetic body 1m is divided into minute elements. An arrow indicates micro-magnetization. The micro-magnetization is disposed in each element, and the state of micro-magnetization of each element is calculated.
In the micro-magnetic simulation, magnetic energy Etotal which is the total energy in a system is denoted by the following expression 1.Etotal=Eani+Eexc+Eappl+Estatic  (1)
Here, Eani is anisotropic energy, Eexc is exchange energy, Eappl is Zeeman energy, and Estatic is magnetostatic energy. Furthermore, in order to limit the format, herein, bold face and italic face are not used. The energies are respectively denoted by the following expressions.
                              E          ani                =                  ∫                      dV            ⁢                                                  ⁢                                          K                u                            ⁡                              (                                  1                  -                                                            (                                              k                        ·                        m                                            )                                        2                                                  )                                                                        (        2        )                                          E          exc                =                  ∫                      dV            ⁢                                                  ⁢            A            ⁢                          {                                                                    (                                          ∇                                              m                        X                                                              )                                    2                                +                                                      (                                          ∇                                              m                        y                                                              )                                    2                                +                                                      (                                          ∇                                              m                        Z                                                              )                                    2                                            }                                                          (        3        )                                          E          appl                =                  -                      ∫                          dV              ⁢                                                          ⁢                              M                s                            ⁢                                                H                  appl                                ·                m                                                                        (        4        )                                          E          static                -                              1            2                    ⁢                      ∫                          dV              ⁢                                                          ⁢                              M                s                            ⁢                                                H                  static                                ·                m                                                                        (        5        )                                          H          static                =                  -                      ∇            ϕ                                              (        6        )            
Here, m is a magnetization vector, mx is an X component of the magnetization vector, my is a Y component of the magnetization vector, mz is a Z component of the magnetization vector, k is a magnetic anisotropic vector, Ku is a magnetic anisotropic constant, A is an exchange coupling constant, Ms is saturation magnetization, Happl is an external magnetic field vector, φ is a static magnetic field potential, and Hstatic is a static magnetic field vector.
Then, the static magnetic field potential ϕ is obtained from the following relational expression.Δϕ=−∇m  (7)
Among the variables described above, variables which are planned to be set in advance at the time of initiating the calculation are m, k, Ku, A, Ms, and Happl.
In a case where the energies described above are calculated by using a finite element method, a time desired for obtaining the static magnetic field potential ϕ occupies the majority of a calculation time. This is because in a case where Expression (7) is numerically dissolved, calculation of dissolving a linear simultaneous equation is performed, and thus, a calculation amount considerably increases.
In analysis of the magnetic body, a steady state frequently gives important information relevant to magnetic physical properties. The steady state of the magnetic body is able to be considered as a state in which total energy in the system described above is minimized. Accordingly, when a micro-magnetization state minimizing the total energy in the system is obtained, the steady state of the magnetic body is able to be reproduced. A method of obtaining the micro-magnetization state for minimizing the total energy of the magnetic body is referred to as an energy minimization method.
Inputs to a micro-magnetic simulation program using the energy minimization method (that is, data that a user prepares in advance) is the model of the magnetic body divided into elements, an initial state of the magnetization vector of each element, and the external magnetic field vector. Output from the micro-magnetic simulation program is the state of the magnetization vector of each element which minimizes the magnetic energy.
International Publication Pamphlet No. WO2014/033888, Japanese Laid-open Patent Publication No. 2012-33116, Japanese Laid-open Patent Publication No. 2013-131072, and Japanese Laid-open Patent Publication No. 2006-53908 are examples of related art.